You have complete freedom to choose the set of operators you want to replace. You may make the decision to replace some operators with custom CUDA kernels and leave others unchanged. You may replace multiple operators with custom implementations, consider operator fusion opportunities (combining multiple operators into a single kernel, for example, combining chunk+gelu+elementwise_mul), or algorithmic changes (such as optimized memory access patterns). You are only limited by your imagination.


CUDA kernel for Focal Tversky Loss with shared memory parallel reduction.

Optimizations:

Stable sigmoid with exp(-|x|).

Shared memory tree reduction for three concurrent sums: TP, FP, FN.

Batch-level parallelism (one block per sample).

Double precision for accuracy.

Kernel computes per batch:

TP = Σ(p * y) (True Positives)

FP = Σ(p * (1-y)) (False Positives)

FN = Σ((1-p) * y) (False Negatives)

Tversky Index:
TI = (TP + smooth) / (TP + α·FN + β·FP + smooth)

Focal Loss:
L = mean((1 - TI)^γ)

Specialized for imbalanced segmentation with adjustable α, β for FP/FN trade-off, and γ for focal weighting.


Here's an example to show you the syntax of inline embedding custom CUDA operators in torch: The example given architecture is:
import torch
import torch.nn as nn
import torch.nn.functional as F


class Model(nn.Module):

    def __init__(self, alpha=0.7, beta=0.3, gamma=0.75, smooth=1.0):
        super().__init__()
        self.alpha = alpha
        self.beta = beta
        self.gamma = gamma
        self.smooth = smooth

    def forward(self, logits: torch.Tensor, targets: torch.Tensor) -> torch.Tensor:
        targets_f = targets.float()

        probs = torch.sigmoid(logits)

        probs = probs.flatten(1)
        targets_f_flat = targets_f.flatten(1)

        tp = (probs * targets_f_flat).sum(dim=1)  # True Positive
        fp = (probs * (1.0 - targets_f_flat)).sum(dim=1)  # False Positive
        fn = ((1.0 - probs) * targets_f_flat).sum(dim=1)  # False Negative

        tversky_index = (tp + self.smooth) / (tp + self.alpha * fn + self.beta * fp + self.smooth)

        focal_tversky_loss = torch.pow(1.0 - tversky_index, self.gamma)

        return focal_tversky_loss.mean()


batch_size = 128
feature_dim = 100


def get_inputs():
    logits = torch.randn(batch_size, feature_dim, dtype=torch.float64)
    targets = torch.randint(0, 2, (batch_size, feature_dim), dtype=torch.float64)
    return [logits, targets]


def get_init_inputs():
    return [0.7, 0.3, 0.75, 1.0]